PN Junction Space Charge Width & Maximum Electric Field Calculator

PN Junction Space Charge Width & Maximum Electric Field Calculator

Calculate the space charge width and the maximum electric field in a PN junction using the equations:
\[ W = \sqrt{\frac{2\,\epsilon_s\,(\phi_{bi}-V)}{q\,N}} \] and
\[ E_{max} = \sqrt{\frac{2\,q\,N\,(\phi_{bi}-V)}{\epsilon_s}} \] where the net potential is \(\phi_{bi}-V\).

* Enter all values in SI units.

Step 1: Enter Parameters

Example: 1.04e-10 F/m (for silicon)

Example: 0.7 V

Example: 0 V (reverse bias)

Example: 1e23 m\(^{-3}\)

Formulas:
\( W = \sqrt{\frac{2\,\epsilon_s\,(\phi_{bi}-V)}{q\,N}} \) and \( E_{max} = \sqrt{\frac{2\,q\,N\,(\phi_{bi}-V)}{\epsilon_s}} \)


Practical Example:
For \(\epsilon_s = 1.04 \times 10^{-10}\) F/m, \(\phi_{bi} = 0.7\) V, \(V = 0\) V, and \(N = 1 \times 10^{23}\) m\(^{-3}\):

Space Charge Width:
\[ W = \sqrt{\frac{2 \times 1.04 \times 10^{-10} \times 0.7}{1.602 \times 10^{-19} \times 1 \times 10^{23}}} \approx 9.54 \times 10^{-8}\, \text{m} \quad (0.0954\,\mu\text{m}) \]

Maximum Electric Field:
\[ E_{max} = \sqrt{\frac{2 \times 1.602 \times 10^{-19} \times 1 \times 10^{23} \times 0.7}{1.04 \times 10^{-10}}} \approx 1.47 \times 10^{7}\, \text{V/m} \]